Question: Solve for $a$, $ -\dfrac{7}{25a^3} = -\dfrac{2a + 3}{20a^3} - \dfrac{3}{15a^3} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25a^3$ $20a^3$ and $15a^3$ The common denominator is $300a^3$ To get $300a^3$ in the denominator of the first term, multiply it by $\frac{12}{12}$ $ -\dfrac{7}{25a^3} \times \dfrac{12}{12} = -\dfrac{84}{300a^3} $ To get $300a^3$ in the denominator of the second term, multiply it by $\frac{15}{15}$ $ -\dfrac{2a + 3}{20a^3} \times \dfrac{15}{15} = -\dfrac{30a + 45}{300a^3} $ To get $300a^3$ in the denominator of the third term, multiply it by $\frac{20}{20}$ $ -\dfrac{3}{15a^3} \times \dfrac{20}{20} = -\dfrac{60}{300a^3} $ This give us: $ -\dfrac{84}{300a^3} = -\dfrac{30a + 45}{300a^3} - \dfrac{60}{300a^3} $ If we multiply both sides of the equation by $300a^3$ , we get: $ -84 = -30a - 45 - 60$ $ -84 = -30a - 105$ $ 21 = -30a $ $ a = -\dfrac{7}{10}$